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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 13

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Answer: -\frac{\cos^{5}x}{5}+c

Hint: You must know about the integration rule of trigonometric function.

Given: \int \cos^{4}x\sin x dx

Solution:  put \cos x =t  differentiate both sides,  \left [ \frac{d}{dx}\cos x= -\sin x \right ]

               -\sin x dx=dt

                 sin xdx=-dt

\therefore I= \int -t^{4} dt                                                                \left [ \int x^{n} dx= \frac{x^{n+1}}{n+1} \right ]

  = \frac{-t^{5}}{5}+c

= \frac{-\cos^{5}x}{5}+c

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